Handbook of Turbomachinery Second Edition Revised - Ventech!

Figure 3 Elliptic lateral whirl.
average processional rate over a complete orbit is equal to the whirl
frequency of the orbit.
Differentiation of Eq. (1) twice with respect to time provides the x- and
y-components of the acceleration for point p. These components are equal to
negative the square of the whirl frequency times the displacement
components. Thus, the acceleration of point p is always directed toward
the center of the elliptical orbit (the negative radial direction), and the
transverse acceleration component is always zero. The type of elliptical
lateral motion described by Eq. (1) is referred to as elliptic vibration. The
elliptical nature of steady rotor motion is caused by stiffness and/or damping
forces that are not isotropic, i.e., the stiffness in the horizontal direction may
be different than in the vertical direction. If all support properties are
isotropic, the steady elliptic motion degenerates to circular motion.
Two special cases of elliptic vibration occur quite often in the
observation of rotor motion. These two cases are referred to as forward
circular whirl and backward circular whirl. Forward circular whirl is the
normal motion of a rotor. Backward circular whirl, however, occurs
infrequently except for systems that have coupled counter-rotating
assemblies.
Forward Circular Whirl. This special whirl condition exists when us ¼ vc
and vs ¼ uc. For illustration purposes, let uc ¼ f and vc ¼ g. The orbit Eq.
(1) then simplifies to
uðtÞ ¼f cos ot g sin ot
vðtÞ ¼ g cos ot þ f sin ot
and describes aforward-whirl circular orbit as illustrated in Fig. 4(a). For
this case, the precessional rate of the radius vector op is constant over the
orbit and is equal to the whirl frequency, o, of the orbit.
Copyright © 2003 Marcel Dekker, Inc.
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